A spline smoothing homotopy method for nonlinear programming problems with both inequality and equality constraints

Abstract

In this paper, we construct a new spline smoothing homotopy method for solving general nonlinear programming problems with a large number of complicated constraints. We transform the equality constraints into the inequality constraints by introducing two parameters. Subsequently, we use smooth spline functions to approximate the inequality constraints. The smooth spline functions involve only few inequality constraints. In other words, the method introduces an active set technique. Under some weaker conditions, we obtain the global convergence of the new spline smoothing homotopy method. We perform numerical tests to compare the new method to other methods, and the numerical results show that the new spline smoothing homotopy method is highly efficient.